Question

Barney goes to the bank with 1000 - $1 bills and 10 paper bags. His instructions to the teller are to place the bills in the bags in such a way that when he returns later, he can request any amount of money from $1 to $1000 and the teller must be able to give him the money without opening any of the bags. What amount of money goes into each of the 10 bags?

I think (and others) that maybe something to do with scientific notation? But I don't understand completely.

Answer 1

Any number from 1 to 1023 can be written as a combination of
1,2,4,8,16,32,64,128, 256 and 512. These are the powers of 2 from 2^0 to 2^9. Just convert it to binary form and that converted number will tell you how many of each bag is needed.
DECIMAL/BINARY
1 = 0000000001 (1 bag of 1)
2 = 0000000010 (1 bag of 2)
3 = 0000000011 (1 of 1 and 1 of 2)
4 = 0000000100 (1 of 4)
33 = 0000100001 (1 of 32 and 1 of 10
1000 = 1111101000
(1 each of 512,256,128,64,32 and 8)